1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
/*
Copyright (C) 2016 Shivin Srivastava
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "fmpz_poly.h"
void _fmpz_poly_fibonacci(fmpz * coeffs, ulong n)
{
fmpz * r;
int even;
ulong k, L;
if (n == 0) return;
if (n == 1)
{
fmpz_one(coeffs);
return;
}
L = n / 2;
even = 1 - (n % 2);
/* set the first two coefficients of poly depending parity of n */
if (even)
{
fmpz_zero(coeffs);
fmpz_one(coeffs + 1);
fmpz_mul_ui(coeffs + 1, coeffs + 1, L);
}
else
{
fmpz_one(coeffs);
fmpz_zero(coeffs + 1);
}
fmpz_one(coeffs + n - 1);
r = coeffs + even;
r += 2;
/* calculate the coefficients of the polynomial*/
for (k = 2 + even; k < n - 2; k += 2)
{
fmpz_mul2_uiui(r, r - 2, L + k / 2, L + k / 2 - k + 1);
fmpz_divexact2_uiui(r, r, k, k - 1);
r += 2;
}
/* set the alternate coefficients to 0 again depending on the parity*/
for (k = 1 + even; k < n; k += 2)
{
fmpz_zero(coeffs + k);
}
}
void fmpz_poly_fibonacci(fmpz_poly_t poly, ulong n)
{
fmpz_poly_fit_length(poly, n);
_fmpz_poly_fibonacci(poly->coeffs, n);
_fmpz_poly_set_length(poly, n);
}